This invention relates to a quadrature-phase amplitude modulating (often abbreviated to QAM) system and a quadrature-phase amplitude demodulating system for use as a counterpart of the modulating system.
In the QAM system, a pair of quadrature-phase carrier signals are amplitude modulated by a first and a second digital input signal into a quadrature-phase amplitude modulated signal of a certain transmission power. When each of the first and the second digital input signals is an i-bit binary signal, the digital input signal is capable of representing at most N levels where N is equal to 2.sup.i. The quadrature-phase amplitude modulated signal becomes an M-ary or multiple quadrature-phase amplitude modulated signal, namely, has M signal points on a phase plane which has an origin and real and imaginary axes crossing at the origin. The M signal points are arranged uniformly in a square having a center at the origin and sides parallel to the real and the imaginary axes. In other words, the M signal points are arranged in a lattice structure on the phase plane. Such a QAM system is herein called a multiple QAM system.
When transmitted from the QAM system to a quadrature-phase amplitude demodulating system through a transmission medium, the quadrature-phase amplitude modulated signal is inevitably subjected to a symbol error of a certain symbol error rate. The symbol error rate depends on a separation between two adjacent signal points. On the other hand, the transmission power is dependent on a peak amplitude of the quadrature-phase amplitude modulated signal, namely, a distance between the origin and a signal point placed at each vertex of the square. The peak amplitude increases in proportion to an increase of the signal points. It is desirable to reduce the transmission power. The separation, however, decreases and results in an increase of the symbol error rate if the peak amplitude is reduced in order to reduce the transmission power.
A hexagonal signal arrangement is exemplified in an article contributed by Marvin K. Simon and Joel G. Smith to IEEE Transactions on Communications, Vol. COM-21, No. 10 (October 1973), pages 1108 to 1115, under the title of "Hexagonal Multiple Phase-and-Amplitude-Shift-Keyed Signal Sets." The hexagonal signal arrangement is capable of reducing the peak amplitude as small as possible. The hexagonal signal arrangement is, however, hard to realize a circuit for arranging the signal points on the phase plane.